MaplePrimes Questions

What I want to achieve with a command is the following image, in which the elements of a matrix that are not zero are displayed in black

This can be accomplished with the Browse Matrix Dialouge, but I want to make such images part of the worksheet. (Display of the full matrix is important.)
Context: Re-execution of worksheets will allow for quick verification of changes in Jacobians.

I have a closed curve(parameterized by t) with self intersection and I'd like to locate the x-y coordinates of the intersection. fslolve only returns 1 intersection. I've tried to use a finite step method but it is way to slow even with rough stepping and becomes very inaccurate. Does maple have anything built in to handle this?

 

  

Download 111.mwFractional_محلوله.pdf

Hello my friends
How can I write the results inside the Maple code as in the picture? That is, writing the results in terms of gamma and alpha

A python program will output several  adjacency matricies which is to be given as a input to a maplesoft code by writing it to some some kind of  file or so with a sample.

The python file will generate several adjacency matrices need to send it as a input to my maple code

With a small sample codes with interface please.

The help will be surely acknowledged

Hi,

Is there a way to symbolically evaluate this integral?

int(sin(sqrt(-x^2 + 1)), x);

I want to write a program for the time fractional thin film equation to be converted into an ordinary differential equation.

With respect

Any one has a trick to show in Maple that  x + sqrt(-2 + 2*sqrt(4*x^2 + 1))*sqrt(2 + 2*sqrt(4*x^2 + 1))/4; is zero for x<=0?

I'd like to get similar simplication as this below but in Maple, But everything I tried so far did not work. I am sure there is a way in Maple, but have not found it yet.

Below is the Maple worksheet

interface(version)

`Standard Worksheet Interface, Maple 2022.1, Windows 10, May 26 2022 Build ID 1619613`

restart;

r := x + sqrt(-2 + 2*sqrt(4*x^2 + 1))*sqrt(2 + 2*sqrt(4*x^2 + 1))/4;

x+(1/4)*(-2+2*(4*x^2+1)^(1/2))^(1/2)*(2+2*(4*x^2+1)^(1/2))^(1/2)

simplify(r) assuming x<0

x+(1/4)*(-2+2*(4*x^2+1)^(1/2))^(1/2)*(2+2*(4*x^2+1)^(1/2))^(1/2)

simplify(r,symbolic) assuming x<0

x+(1/4)*(-2+2*(4*x^2+1)^(1/2))^(1/2)*(2+2*(4*x^2+1)^(1/2))^(1/2)

simplify(r,sqrt) assuming x<0

x+(1/4)*(-2+2*(4*x^2+1)^(1/2))^(1/2)*(2+2*(4*x^2+1)^(1/2))^(1/2)

#showing it is zero for x<=0
plot(r,x=-10..1)

 

Download show_it_is_zero.mw

how can i plot this complex expression with polar plot and 3d complex plot? i want both 2d polar form and 3d plot of this.
thnx for the help

restart:with(plots,complexplot,implicitplot)

[complexplot, implicitplot]

(1)

f:=(r,theta)->I*sinh(theta-Pi/6)+cos(Pi/4)=r;

proc (r, theta) options operator, arrow; I*sinh(theta-(1/6)*Pi)+cos((1/4)*Pi) = r end proc

(2)

complexplot(f(r,theta), r = 0 .. 1, theta = 0 .. 2*Pi, coords=polar);
 

Error, (in plot) incorrect first argument [1/2*2^(1/2)-Im(sinh(theta-1/6*Pi)) = Re(r), Re(sinh(theta-1/6*Pi)) = Im(r), r = 0 .. 1]

 

 

Download complexplot.mw

I want to find the relation between w and k by putting Determinant(A) is equal to zero. Since the determinant is large (A is a matrix of size 6x6) and I am not able to find the simplified expression. How to do that?

 

determinant.mw

Hi,

I use Maple version 2022.1 on macOS 10.14.6.

I have big problems with the parabolic groups in the "LieAlgebra" package.

First of all in the help for "Query > Parabolic", the link refers to the help page for the commands "CylinderU, CylinderV, CylinderD" which have nothing to do with it. Also, the command "Query(Alg, "Parabolic")" does not work.

Below is a list of commands that give an error for "Query".

restart:with(LinearAlgebra):with(DifferentialGeometry):with(LieAlgebras):

L:=[
Matrix(5, 5, [[0, 0, 1, 1, 1], [0, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0]]), 
Matrix(5, 5, [[0, 1, 0, 1, 1], [-1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0]]), 
Matrix(5, 5, [[0, 1, 1, 0, 1], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-1, 0, 0, 0, 0]]), 
Matrix(5, 5, [[0, 1, 1, 1, 0], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [0, 0, 0, 0, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 0], [0, -1, 0, 0, 0], [0, -1, 0, 0, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 1, 0, 1], [0, -1, 0, 0, 0], [0, 0, 0, 0, 0], [0, -1, 0, 0, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 1, 1, 0], [0, -1, 0, 0, 0], [0, -1, 0, 0, 0], [0, 0, 0, 0, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, -1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 0, 0, 0], [0, 0, -1, 0, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, -1, 0, 0], [0, 1, 0, 1, 0], [0, 0, -1, 0, 0], [0, 0, 0, 0, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, -1, 0], [0, 1, 1, 0, 0], [0, 0, 0, 0, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, -1, 0, 0], [0, 0, -1, 0, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, -1, 0], [0, 0, 1, 0, 1], [0, 0, 0, -1, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 1, 1, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 0, -1, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0], [0, 0, 0, 0, -1], [0, 1, 0, 1, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0], [0, 1, 1, 0, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, -1/2*sqrt(2), -1/2*sqrt(2), -1/2*sqrt(2)], [0, 1/2*sqrt(2), 0, 0, 0], [0, 1/2*sqrt(2), 0, 0, 0], [0, 1/2*sqrt(2), 0, 0, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 1/2*sqrt(6), 1/6*sqrt(6), 1/6*sqrt(6)], [0, -1/2*sqrt(6), 0, -1/3*sqrt(6), -1/3*sqrt(6)], [0, -1/6*sqrt(6), 1/3*sqrt(6), 0, 0], [0, -1/6*sqrt(6), 1/3*sqrt(6), 0, 0]]), 
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 2/3*sqrt(3), 1/6*sqrt(3)], [0, 0, 0, 2/3*sqrt(3), 1/6*sqrt(3)], [0, -2/3*sqrt(3), -2/3*sqrt(3), 0, -1/2*sqrt(3)], [0, -1/6*sqrt(3), -1/6*sqrt(3), 1/2*sqrt(3), 0]]), Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*sqrt(5)], [0, 0, 0, 0, 1/2*sqrt(5)], [0, 0, 0, 0, 1/2*sqrt(5)], [0, -1/2*sqrt(5), -1/2*sqrt(5), -1/2*sqrt(5), 0]])];

LieP:=LieAlgebraData(L,Alg):
DGsetup(LieP);
Query(Alg,"Parabolic");

 

Let G(V,E)  be a graph

 Step 1 : Choose the subsets S of the V of size k and LABEL it with the say "1"

Step 2: LABEL all the neighbours of the vertices of S with "1"

Step 3: Now LABEL "1" all the UNLABELED neighbours of the previously LABELED veritices only if its neighbours are all LABELED already

Step 4: IF atleast one vertex is LABELED in step 3 then repeat step 3   ELSE  If all vertices are already LABELED with "1" goto step 5 ELSE if some of the VERTICES are still not LABELED we reject this set GOTO step 6

Step 5: append the the the set S into the list 

Step 6: Remove all the perivious labels choose a new set of size k from S label its vertices with "1" and goto step 2  if all all sets of size k have already been choosen we end and print the list.

That is we a Function F(Graph::G,k)     the function which does the above so that it can be called with parameter when required for any graph G

I am going to try too but i am not that great at coding I have desinged the algorithm need help if possible kind help

I will also be trying 

I apologize to distrub all in your busy schedule.

Your work will be surely acknowledged 

First_sample_1.mw

 

https://www.mapleprimes.com/questions/234533-How-To-Relabel-Only-A-Subset-Of-Vertex-Of-G#comment287899

 

Some part in above link

In code attached 

I would like to 

I have to on say L list.

And I have done steps at the top in that code

After the above code I have attached steps

"Find the vertices with the condition that if  all its neighbors are labeled as character (FIND(G)) then label those vertices  also as `character"`  then add those vertices also to  L1 list"  then Need to be do again and again on the same graph with new labels G

If no such vertex exits and NumberOfVertices(G) not equal to numelems(L1) then i have to break out of the loop.

or 

if NumberOfVertices(G)=numelems(L1) then I print That list or store it some where

Please pardon me if my english is bad.

KInd help it will help me a lot and it will surely be acknowledged kind help.

 

The algorithm all told above kind help please please

The help will be surely acknowledged

 

 

 

Hello everyone,

I'm not quite sure, if this is the correct place but i think i found a bug in the analytic integration tool in Maple.

Since i have the student edition and i didn't find a bug report form i will post it here:

restart:

R:=1:
delta:=1:

f:=R^4*delta*cos(theta)*sin(x)*sin(-x+theta)/(8*Pi*(R^2*cos(x)+sqrt(2*R^2*cos(x)+2*R^2+4*delta^2)*delta+R^2+2*delta^2));


intfAna:=int(f,x= -Pi + theta .. Pi+ theta);

intfNum:=Int(f,x= -Pi + theta .. Pi+ theta);
intNum:=evalf(Int(eval(intfNum),theta=0..2*Pi));
intAna:=evalf(int(eval(intfAna),theta=0..2*Pi));

the last two statements yield:

                    intNum := -0.07343950362
                    intAna := -0.7853981635

Thus the numerical integrated value differes from the analytical result.

Since I also tried to integrate this with scipy in python I'm pretty sure that the numerical result is correct  and the analytical one is not.

Is my deduction here correct?

I have Maple 2018 here on my private PC. But at work i have Maple 2021 and the difference is the same.

 

Interestingly the analytic result seems to be -cos(theta)^2/4. If we plot the analytical and numerical integrand, we get:

plot(intfNum,theta=0..2*Pi);
plot(intfAna,theta=0..2*Pi);

 

Thus both integrands seem to be cosines of theta but the analytical has the wrong factor.

Thanks in advance!

Give a graph G enumerate all possible shortest paths from that vertex to all other vertices like

From vertex v1

P1={(1,2),(2,3)} shortest path from 1 to 3 is stored in P1

P2={(1,2)} shortest path from 1 to 2 of length 1 

Put all possible path of length k  from a verex v in a list seperate

That is length 1 in a seperate from vertex v in a seperate list 

Etc

Function with be F(Graph::G,v)

Function will return all those lists

restart;
with(GraphTheory);
with(combinat, cartprod);
with(SpecialGraphs);
with(RandomGraphs);

Given any arbitary graph G how many possible paths of length k are possible

G := CartesianProduct(PathGraph(3), PathGraph(3));
s := AllPairsDistance(FLT)

How to find how may possible paths of length say 4 from vertex 1:1 

" for example this CartesianProduct(Path(3),Path(3)) number of possible paths of length 2 are

1:1 - 1:2 -2:2

1:1 -2:1-2:2

1:1-1:2 -1:3

1:1-2:1-3:1

so a total of 2 length paths 

next say how may possible paths of length say 3 from vertex 1:2

similar given a vertex and path length how many possible path of that length are possible from that vertex.

It is not restricted to this graph given any graph G in general , a vertex v and k a path length i should get total number of paths of that length in that graph G

That is function say   F(G::Graph,vertex,k) i should get output of the number of path of length k from that vertex v. 

"Only a idea but I may be wrong 

I had an idea taking a row of a vertex in the graph G in the shortest path matrix and finding the number of possible totals which can get  length k I may be wrong to or correct but I finding to implement this in code neatly too.

That is if (0,1,2,1,3,4,1,2)

The number of possible 2 this are 

0+2=2

0+2=2

1+1=2

1+1=2

1+1=2

So a total of 5 , 2 length path with respect to that vertex moving from left to right

Again if number of 3 length paths 

Moving left to right

0+3=3

1+2=3

1+1+1=3

1+2=3

2+1=3

2+1=3

1+2=3

1+2=3

Total 8 paths of length 3

Until maximum possible length path from that vertex with respect to that graph.

Their is a mistake in the above logic is if the length paths intersection in some edges the path length will decrease so need to be careful so it looks difficult for me.

But I may be wrong in logic need help."

I am trying too

Kind help please your answer will be acknowledged 

Kind help 

Kind help someone please 

I use Int to show some step before evaluating it to become normal int

I'd like to show the following when the integrand is one:

But Int(x) does not work, and Int(,x) gives syntax error. So only choice is to use Int(1,x) which does not look as nice as the above

Is there a trick to use? i.e. when the integrand is one, I want to display it as the first image and not as the second image. This is just to make the Latex look a little nicer only.

I tried few things, but nothing worked so far, as Int needs something there where I want the empty spot to be (There is actually 1 there ofcourse, but I do not want to show the 1).

May be we need a Latex settings for this?  Or interface setting?

Maple 2022.1

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